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  3. Metric Diophantine Approximation on Manifolds
  • Cited by 97
Publisher:
Cambridge University Press
Online publication date:
August 2010
Print publication year:
1999
Online ISBN:
9780511565991
DOI:
https://doi.org/10.1017/CBO9780511565991
Subjects:
Mathematics (general), Mathematics, Number Theory
Series:
Cambridge Tracts in Mathematics (137)
Information

Book description

This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. After setting out the necessary background material, the authors give a full discussion of Hausdorff dimension and its uses in Diophantine approximation. A wide range of techniques from the number theory arsenal are used to obtain the upper and lower bounds required, and this is an indication of the difficulty of some of the questions considered. The authors go on to consider briefly the p-adic case, and they conclude with a chapter on some applications of metric Diophantine approximation. All researchers with an interest in Diophantine approximation will welcome this book.

Reviews

‘This book is an important addition to the literature from authors who are leading experts in this field.’

Glyn Harman Source: Bulletin of the London Mathematical Society

‘… carefully written, with an extensive bibliography, and will be of lasting value …’.

Thomas Ward Source: Zentralblatt für Mathematik

‘This book can be recommended not only to those interested in number-theoretic aspects, but also to those interests lie in topics related to dynamical systems … self-contained and very readable.’

Source: EMS

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